Problem: 3 people can paint 7 walls in 33 minutes. How many minutes will it take for 7 people to paint 8 walls? Round to the nearest minute.
Explanation: We know the following about the number of walls $w$ painted by $p$ people in $t$ minutes at a constant rate $r$ $w = r \cdot t \cdot p$ $\begin{align*}w &= 7\text{ walls}\\ p &= 3\text{ people}\\ t &= 33\text{ minutes}\end{align*}$ Substituting known values and solving for $r$ $r = \dfrac{w}{t \cdot p}= \dfrac{7}{33 \cdot 3} = \dfrac{7}{99}\text{ walls painted per minute per person}$ We can now calculate the amount of time to paint 8 walls with 7 people. $t = \dfrac{w}{r \cdot p} = \dfrac{8}{\dfrac{7}{99} \cdot 7} = \dfrac{8}{\dfrac{49}{99}} = \dfrac{792}{49}\text{ minutes}$ $= 16 \dfrac{8}{49}\text{ minutes}$ Round to the nearest minute: $t = 16\text{ minutes}$